Among the 1018 respondents, 179 said that cellular phones are “not at all annoying”.

The line L is a tangent to the curve with equation y= 4x^2 +1 . The line L cuts the y axis at (0,8) and has a positive gradient.

sergeinik [125]

A generic point on the graph of the curve has coordinates

$(x, 4x^2+1)$

The derivative gives us the slope of the tangent line at a given point:

$f(x) = 4x^2+1 \implies f'(x) = 8x$

Let k be a generic x-coordinate. The tangent line to the curve at this point will pass through $(k, 4k^2+1)$ and have slope $8k$

So, we can write its equation using the point-slope formula: a line with slope m passing through $(x_0, y_0)$ has equation

$y-y_0 = m(x-x_0)$

In this case, $(x_0, y_0)=(k, 4k^2+1)$ and $m=8k$ , so the equation becomes

$y-4k^2-1 = 8k(x-k)$

We can rewrite the equation as follows:

$y-4k^2-1 = 8k(x-k) \iff y = 8kx - 8k^2+4k^2+1 \iff y = 8kx-4k^2+1$

We know that this function must give 0 when evaluated at x=0:

$f(x) = 8kx-4k^2+1 \implies f(0) = -4k^2+1 = 8 \iff -4k^2 = 7 \iff k^2 = -\dfrac{7}{4}$

This equation has no real solution, so the problem looks impossible.

5 0

3 years ago

The difference of a number T and 7 is greater than 10 and less than 20

natulia [17]

The answer is 20>t-7>10

5 0

3 years ago

Line CD contains points A (4, 6) and B (−2, 6). The slope of line CD is (4 points)

lbvjy [14]

Answer:

0

Step-by-step explanation:

To find the slope, we use the formula

m= (y2-y1)/(x2-x1)

= (6-6)/(-2-4)

= 0/-6

=0

8 0

3 years ago

Suppose that two electronic components in the guidance system for a missile operate independently and that each has a length of

lord [1]

Answer:

The probability density function for the average length of life of the two components is $f(x) = 0.5e^{-0.5x}$

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following probability density:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

Each missile has a length of life governed by the exponential distribution with mean 1 (with measurements in hundreds of hours). Find the probability density function for the average length of life of the two components.

2, each with mean 1 means that $m = 2*1 = 2, \mu = \frac{1}{2} = 0.5$

So the probability density function is:

$f(x) = 0.5e^{-0.5x}$

8 0

2 years ago

ahmed is working at a burger joint. his boss pays him $5.50 per hour and promises a raise of $0.25 per hour every 6 months. whic

nasty-shy [4]

Well if hes gonna add .25 cents every 6th month then i think you would have to pick D because it shows the starting pay (5.50) then adds the .25 for every 6th month. Hope i helped :)

7 0

3 years ago

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